Question

Don uses his small motorboat to go 4 miles upstream to his favorite fishing spot. Against the current, the trip takes `1/2` hour. With the current, the trip takes `1/4` hour. How fast can the boat travel in still water? What is the current's speed?

Answer 1

Speed of boat=12 miles per hour
Speed of current = 4 miles per hour

Explanation:

Let speed of motorboat be x
Speed of current be y

During downstream,
Distance=4 miles.
Time = `1/4`hours
Speed=x+y(with the current)
Distance/time = x+y
`4/0.25 = x+y`
16 = x+y

During upstream,
Distance=4 miles
Time=`1/2` hours
Speed=x-y(against the current)
`4/0.5`= x-y
8 = x-y

From these two equations you can calculate the value of x and y that are 12 and 4 respectively .

Hope it helps you

Answer 2

The boat's speed (on still water) is at `12` miles per hour and the current speed is at `4` miles per hour.

Explanation:

We know that distance equals to speed multiplied by time.

In the problem, Don has to go `4` miles upstream. Thus, the distance traveled is `4`.

While going upstream, the time taken is `1/2` hours. Suppose that his speed is `d` and the current's speed is `c`. Since he is going against the current, the net speed is `d-c`. Thus, `4=1/2*(d-c)`.

While going downstream, the time takes `1/4` hours. Supposing again that his speed is `d` and the current's speed is `c`, going with the current means that the net speed is `d+c`. Thus, `4=1/4*(d+c)`.

So now we have two simultaneous equations:
`{(4=1/2*(d-c)=1/2*d-1/2*c),(4=1/4*(d+c)=1/4*d+1/4*c):}`

Multiply both sides of the second equation by `2` and add the first and second equation, eliminating the constant `c`:
`4+4*2=1/2*d-1/2*c+2*(1/4*d+1/4*c)`
`12=d`

Since the first equation states that `4=1/2*d-1/2*c)`, substituting the known value `d=12` reveals that `4=1/2*12-1/2*c`, or `c=4`.

Thus, we have the boat's speed (on still water) at `12` miles per hour and the current speed at `4` miles per hour.